Let the operators \(z^{H_0}\)  and \(e^K\)  are defined the same as that in [1]}. Then define
\(\Psi (z)&=&\sum _{j\in \mathbb {Z}+\frac{1}{2}}\Psi _jz^{-j-1/2}=e^{\left(\sum _{n\ge 1}\frac{x_n}{\sqrt{\alpha }}z^{n}\right)}e^{\left(-\sum _{n\ge 1}{\partial _{p_n}}\sqrt{\alpha }z^{-n}\right)}e^Kz^{H_0},\\\Psi ^*(z)&=&\sum _{j\in \mathbb {Z}+\frac{1}{2}}\Psi _j^*z^{-j-1/2}=e^{\left(-\sum _{n\ge 1}\frac{x_n}{\sqrt{\alpha }}z^{n}\right)}e^{\left(\sum _{n\ge 1}{\partial _{p_n}}\sqrt{\alpha }z^{-n}\right)}e^{-K}z^{-H_0}.\) 
